Upon direct contact, Sayaka can acquire a copy of the magical ability of the magical girl she touched, which appears to be identical to the original magic in terms of both versatility and strength. She does not gain any intrinsic skill in this power, and even the "base instincts" that are normally available to a magical girl after making her wish are noticeably dulled.
She is capable of turning a power she currently has "equipped" into a gem-like shape for storage. She can, by touching one of these gems, re-acquire the ability as if she had copied it from its original owner again. These gems have the same color as Sayaka's soul gem, but the same shape as the soul gem of the girl she copied it from. The thematics of the copied powers are altered to match Sayaka's color scheme and outfit, for instance her copies of Mami's ribbons are naturally white, not yellow. There is a faint echo of Sayaka's witch inside each of her power storage gems.
While Sayaka has a copied power "equipped", there is a constant drain on her soul gem, in addition to the drain imposed by using her copied powers abilities. Sayaka is capable of maintaining multiple active powers simultaneously. The largest amount she was able to have running at once so far is five. When she had five powers active at once, she found it hard to control them, accidentally activating portions of powers other then the power she intended to use. There was no difference in terms of drain on her soul gem between maintaining one power, and two powers.
Sayaka's copy of the cloning power she acquired from Ishinomaki provides her with multitasking. With that multitasking, she's able to fairly easily maintain clones with distinct power-sets. It's likely that other multitasking powers would have similar effects on her ability to run multiple powers at once. Sayaka is able to, to some extent, "combine" magics, allowing aspects of one magical ability she has manifested to apply to others.
Sayaka has been unable to copy Sabrina's power. It's unknown if this is also the case for any other powers. Sayaka was able to copy Rionna Mag Aoidh's power, showing that she can copy from unwilling (or perhaps unconscious) targets.
Ribbons: Tomoe Mami
Conduct Magic, allow for longer range use of other powers.
Antimagic: Kirika Kure
Oh hell yes.
Healing: Chitose Yuma
Powerful healing, can regenerate missing limbs in seconds.
Cloning: Koizumi Aki
Clow Card #15: The Twin
Improves with practice, reduces multitasking strain. Extremely synergistic with copying.
Geokinesis: Inoue Yuuna
Clow Card #52: The Earthy
Lightning: Sato Kimiko
Clow Card #42: The Thunder
Visual Prowess: Ueda Miyako
Hypnosis: Kagome Ayaka
Clow Card #34: The Sleep
Flight: Tsubaki Chouko
Clow Card #41: The Fly
Semi-redundant, as Sayaka can already fly.
Plant Control: Suzuki Haru
Clow Card #16: The Wood
Paper Control: Suzuki Rei
Surprisingly useful, according to Sayaka.
If nothing else, makes for a sweet Konan cosplay.
Invisibility: Umeko Yuko
Clear Card: Lucid
Illusory Copying: Kazusa Michiru
Clow Card #3: The Illusion
Yo dawg, I heard you like copying powers...
True Writing: Umika Misaki
Animal Speech: Satomi Usagi
"Don't fuck with squirrels, Morty!"
Physical Boost/Heals: Kaoru Maki
Clow Card #34: The Power
Healing is limited.
Transmutation: Niko Kanna
Clow Card #37: The Create
Lightning Statuses: Saki Asami
Lightning based Hastaga/Slowaga, Lightning teleportation, etc
Unstoppable: Nadia Bennouna
Useful so she can imitate the Kool-Aid Man.
Soul Claiming: Rionna Mag Aoidh
Sabrina's hanging on to the power gem.